Abstract: This talk will include 1) a pedagogical description of the tools that one uses to construct a quantum simulation and 2) demonstrations of their use to implement quantum simulations on modern quantum computers, which do not yet have significant error correcting capabilities. The tools that I’ll discuss are largely related to operator splitting methods. These are ways to approximate complex Hamiltonian evolution by interleaving simpler evolutions that can be readily computed. The discussion of operator splitting methods will be sufficient for understanding the simulation of time-independent Hamiltonian evolution. However, I’ll also introduce a few more tools, including Magnus series methods, in order to attack the time-dependent problem. During the talk, I’ll demonstrate the application of these methods to the quantum simulation of tunneling phenomena and to molecular collisions using systems of just a few qubits.